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Standard XII

Mathematics

Distinguishing between Conics from General Equation and Eccentricity

If the abscis...

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If the abscissae and ordinates of the ends of a diameter of a circle are the roots of the equations x2-x-1 0 and 2y2+ 3y +1 0 respectively, then the equation of the circle is

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Q. The equation of the circle whose one diameter is

P Q

, where the ordinates of

P, Q

are the roots of the equation

x^{2} + 2 x - 3 = 0

and the abscissae are the roots of the equation

y^{2} + 4 y - 12 = 0

, is

Q. If the abscissaes and ordinates of two points

P

and

Q

are the roots of the equations

x^{2} + 2 a x - b^{2} = 0

and

x^{2} + 2 p x - q^{2} = 0

respectively, then equation of the circle with

P Q

as diameter is

The abscissa and ordinate of the points A and B are the roots of the equation $x^{2} + 2 a x + b = 0$ and $x^{2} + 2 c x + d = 0$ respectively, then equation of circle with AB as diameter is

Q. If the abscissae of points

A, B

are the roots of the equation

x^{2} + 2 a x - b^{2} = 0

and ordinates of

A, B

are roots of

y^{2} + 2 p y - q^{2} = 0

, then find the equation of a circle for which

¯ ¯¯¯¯¯¯ ¯ A B

is a diameter

Q. The abscissae and ordinates of the endpoints

A

and

B

of a focal chord of the parabola

y^{2} = 4 x

are respectively, the roots of equations

x^{2} - 3 x + a = 0

and

y^{2} + 6 y + b = 0

. The find the equation of the circle with

A B

as diameter.

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